Page 13 - Make a 3D-tiling: One, two, four and eight SF blocks, copied in 3 directions along rhombohedron raster.

Page 14 - One more example of a 3D tiling: SF #14

Page 15 - The 54 different Polyhedra

Page 16 - The 42 different Spacefillers

Page 17 - All the 16 SF’s made by one kind of nest.

Page 18 - SF animations of SF01-SF14

Page 19 - SF animations of SF15-SF28

Page 20 - SF animations of SF29-SF42

Page 21 - Z-Patterns of nests

Page 22 - Some statistics and the structure-graph

Page 23 - 3 Tables with details of: Spacefillers, Polyhedra and Nests

Page 24 - Projections of Dual Nets (SF# 1,28,41)

Page 25 - Credits and Acknowledgements

Collection of Spacefillers (SF’s)

Based on this book by Peter Pearce (1978), chapter 8.

Spidronisation of these SF’s gives some new insights into 3D tilings.

More details can be found in our paper published in the Bridges 2009 Conference Proceedings, or click here.

Faces of Saddle Polyhedra can be defined with Skew Polygons.

These can be filled with a minimal surface like a soap film, as Pearce did.

Or with Spidronnests. This introduces an orientation: CW or CCW (clockwise / counter-clockwise)

In general: Nests are the building blocks of Polyhedra, which can be assembled into SF’s, and to (possibly bigger) periodical Units.

Matching nests in the 3D tiling need to have opposite orientations.

Grey: flat

Blue: regular

Red: mirror 4-gon

Purple: mirror 5-gon

Turquoise: mirror 6-gon

Violet: mirror 8-gon

Green: mirror 12-gon

Yellow: enantiomorphic

Method: “scale and rotate”. Nest in general not foldable.

Spidronnest orientations causes doubling compared to Pearce’s SF’s.

Cyan is CCW and Blue is CW. Projection along raster gives 2D-tilings.

(SF’s 1 2 3 4 / 6 9 11 13 / 14 23 24 27 / 28 30 33 39 )

Thanks to Peter Pearce, who described in his great book “Structure in Nature is a Strategy for Design” all the original Spacefillers, based on saddle-surfaces.

Thanks to all other members of the Spidron Team (amongst others: Lajos Szilassi, Rinus Roelofs, Marc Pelletier, Amina Buhler-Allen), for all their inspiring earlier work, including four earlier designs of Spidronised Spacefillers.
(SF’s 2 , 3 , 4 and 5, all based on only regular skew polygons)

Thanks to András Fodor, who made this presentation.

Apart from the abovementioned contributions, all work presented here was made by:
Walt van Ballegooijen, Paul Gailiunas and Dániel Erdély, 2009.

For more information about Spidrons, see the main website: www.spidron.hu.